The strategy to multiply numbers from 11 to 19 quickly in your head is based on the fact that in the traditional way you need to multiply by the tens place value three different times, but with this strategy you cut it down to once. Once you know it you will be so fast people will think you know your time tables up to 19!
Example:
13 x 17
In the traditional way you would stack these numbers one over the other and you would multiply first 3 x 7, then 3 x 1, which is actually 3 x 10 because the 1 is in the tens place. Next you would put down a 0 to show that you are moving from the 3 in the ones place to the 1 in the tens place, and you would multiply 1 x 7, which is actually 10 x 7, and then 1 x 1, which is actually 10 x 10. That is three times you are multiplying by 10. Lets look at that:
3 x 10
10 x 7
10 x 10
We know that with multiplication you can change the order of factors and still get the same product, so lets move the numbers around a little:
3 x10 = 30
7 x 10 = 70
10 x 10 = 100
20 x 10 = 200
As you can see the three steps could be combined, but how? It is really easy just remember these 3 steps:
1. Take the number in the ones position from one of the factors and add it to the other factor, so using our example we could take the 3 from 13 and add it to the 17.
17 + 3 = 20
2. Multiply the result of step one by 10. 20 x 10 = 200. This has now taken care of the three steps discussed earlier.
3. Multiply the numbers in the ones position 3 x 7 = 21, and add to the result of step 2.
The Teens Strategy
The strategy to multiply numbers from 11 to 19 quickly in your head is based on the fact that in the traditional way you need to multiply by the tens place value three different times, but with this strategy you cut it down to once. Once you know it you will be so fast people will think you know your time tables up to 19!
Example:
13 x 17
In the traditional way you would stack these numbers one over the other and you would multiply first 3 x 7, then 3 x 1, which is actually 3 x 10 because the 1 is in the tens place. Next you would put down a 0 to show that you are moving from the 3 in the ones place to the 1 in the tens place, and you would multiply 1 x 7, which is actually 10 x 7, and then 1 x 1, which is actually 10 x 10. That is three times you are multiplying by 10. Lets look at that:
3 x 10
10 x 7
10 x 10
We know that with multiplication you can change the order of factors and still get the same product, so lets move the numbers around a little:
3 x10 = 30
7 x 10 = 70
10 x 10 = 100
20 x 10 = 200
As you can see the three steps could be combined, but how? It is really easy just remember these 3 steps:
1. Take the number in the ones position from one of the factors and add it to the other factor, so using our example we could take the 3 from 13 and add it to the 17.
17 + 3 = 20
2. Multiply the result of step one by 10. 20 x 10 = 200. This has now taken care of the three steps discussed earlier.
3. Multiply the numbers in the ones position 3 x 7 = 21, and add to the result of step 2.
That is it now practice, practice, practice